Jordan fills herself with water and doesn’t eat enough. I’ve prescribed her salt tablets to help prevent water toxicity, but I don’t know if she’s taking them. It may be necessary to place her on a saline drip, but, for reasons I have difficulty expressing, I find I do not believe that medical intervention of that kind would be productive in her case. Her mental acuity is not in any way diminished; in fact, she appears to have entered a manic phase. She is highly excited, irritable, preoccupied. Given her demeanor, I did not expect her to be prepared for another conversation with me, but when we next met, she was eager to talk.

She claims that she has discovered a previously-unknown number. She says she found it “between seven and eight” and calls it “seight,” but insists that it is an integer, a “complete quantity level” which sometimes exceeds the value of eight, while at other times it is inferior in value to seven. She says that seight is a “neutral” number, neither positive nor negative, but unlike zero, it will modify other numbers, such that the sum of seight and another number, or the remainder after seight is subtracted from another number, will, as she put it, appear to be the same as the original number as long as it is used only for usual arithmetical purposes. A number that has been involved in an equation with seight, she claims, can be identified only by its failure to behave as expected when transposed into a different numeral system.

Jordan’s great excitement is prompted by what she claims is the successful unfolding of a project of hers to create a “base seight” numeral system that would, according to her, make an entirely new kind of mathematics possible. She demands the return of her earbuds and a music player to help her concentrate on this work, insisting that the techno song she identified earlier is essential to her progress beyond a certain point. She says that it could help her achieve her goal by maintaining what she calls “base ten thought” for her, prosthetically, so to speak, and thus enable her to devote her entire mind to the transformation procedures for conversion to “base seight.”

When I asked Jordan what she found so exciting about base seight, she first replied in the sort of grandiose terms normally associated with paranoia, to the effect that it would revolutionize mathematics and constituted the first genuine breakthrough at the fundamental level in “millennia.” With further discussion of its importance, however, she then went on to tell me that water machine is programmed in base seight, and that her work will enable her, at last, to establish contact with water machine, because it will restructure her mind to be more “water-machine-compatible.”